Page 234 - Separation process engineering

Example 5-2. Bubble-point calculation

At 1.0 atm, what is the temperature and vapor mole fraction in the reboiler (stage 1) if the bottoms is
15 mol% isopentane, 30 mol% n-pentane, and 55 mol% n-hexane?

Solution

A. Define. We want T for which .
1
B. Explore. To illustrate a trial-and-error procedure, we use the DePriester charts, Figures 2-11 and
2-12. Equation (2-30) could be used instead of the DePriester charts, and we use it for the Check.
First, convert atm to kPa.

p = 1.0 atm(101.3 kPa/1,0atm) = 101.3 kPa
C. Plan. Use the DePriester chart to pick a temperature T for which K > K > 1.0 > K .
1 ic5 nc5 nc6
Calculate the summation in Eq. (5-33), use Eq. (5-34) to calculate K , and find T from the
1
ref
DePriester chart. We pick nC as the reference component because it is the most abundant
6
component. Then repeat the calculation with this new temperature.
D. Do It. First guess: Using Figure 2-12 at 50°C: K = 2.02, K nc5 = 1.55, K nc6 = 0.56. Thus, 50°C
ic5
(and many other temperatures) satisfies our first guess criteria. Calculate stoichiometric sum:

Since the sum is too high, the temperature of 50°C is too high. From Eq. (5-34), calculate

From the DePriester chart, the corresponding temperature is T = 47.5°C. At this temperature, K ic5
1
= 1.92, K nc5 = 1.50. Note that all the K’s are lower, so the summation will be lower. Now the
summation is

The next K = 0.52/1.024 = 0.508, which corresponds to T = 47°C. At this temperature, K =
ic5
c6
1.89, K nc5 = 1.44. The summation is

This is about as close as we can get with the DePriester chart. Thus, T = 47°C.
1
The y values are equal to K x . Thus, y ic5,1 = (1.89)(0.15) = 0.284, y nc5,1 = (1.44)(0.30) = 0.432,
i,1
i,1 i,1
y = (0.508)(0.55) = 0.279. Because of the accuracy of the DePriester charts, the y values
nc6,1 i
should be rounded off to two significant figures when they are reported.
E. Check. An alternative solution can be obtained using Eq. (2-30). First guess: T = 50°C = 122°F =
122 + 459.58 = 581.58°R, and p = 14.7 psia. For iC5, nC5, nC6, Eq. (2-30) simplifies to